By constructing the cohomologies complexes of Rota-Baxter Lie algebra homomorphisms, we discuss the formal deformation of Rota-Baxter Lie algebra homomorphisms and prove that Rota-Baxter Lie algebra homomorphism is rigid when the 2th-cohomology group of the deformation complex is zero.

We discussed the E-total coloring of complete bipartite graphs K_4,n which were vertex-distinguished by multiple sets by using
 the method of proof by contradiction, the method of pre-assignment of color sets and the method of constructing specific coloring, and determined E-total chromatic numbers of K_4,n which were vertex-distinguished by multiple sets.

Let the strong product graph of path P_m and star graph S_1,n-1 be G=P_m*S_1,n-1. Firstly, by inducing assumptions and constructing internally vertex or edge disjoint paths, combined with the centrality of star graph, the vertex fault diameter D_w(G) and edge fault diameter D′_t(G) of the graph G were given. The results show that for any vertex or edge fault in the graph G, there holds D_w(G)≤d(G)+2 and D′_t(G)≤d(G)+1. Secondly, through the unequal relation between the number of vertices and the number of edges, the upper bound of the vertex fault diameter of the strong product graph of two maximally connected graphs and the 
upper bound of the edge fault diameter of the strong product graph of two nontrivial connected graph were given.

By using structural analysis method, we completely characterized the neighbor full sum distinguishing total coloring of unicyclic graph U, and obtained that ftndi_Σ(U)=Δ(U)+2 when U=C_n and n=0(mod 3),  ftndi_Σ(U)=Δ(U)+1 in other cases. This result  shows that the neighbor full sum distinguishing total coloring conjecture  holds on any unicyclic graph.

By using the method of proof by contradiction, the method of pre-assignment of color sets and the method of constructing coloring, we discussed the general total coloring of  complete p-partite graphs which were vertex-distinguished by multiple sets, gave the coloring scheme for optimal coloring and determined the chormatic numbers of the corresponding colorings.

Let R S be a Frobenius extension of rings and M be an S-module. We prove that if R S is a separable Frobenius extension, then _SM is a projectively coresolved GorensteinFI_n-flat module (GorensteinFI_n-flat module) if and only if _RM is a projectively coresolved GorensteinFI_n-flat module (GorensteinFI_n-flat module).

Let (L,A) be a fixed complete duality pair. Firstly, the author introduced the Gorenstein (L,A)-injective dimension of complexes, gave its  characterization, and proved that Gorenstein (L,A)-injective dimension of complexes was not larger than injective dimension. Secondly, the author also discussed relative cohomology and  Tate cohomology of complexes, and obtained the long exact sequence connecting absolute, relative and Tate cohomology.

We gave a Dai-Liao conjugate gradient method based on regularization model. Firstly,  a new Dai-Liao parameter t was obtained by minimizing the 3-degree regularization model, and based  on this, an adaptive Dai-Liao parameter was generated according to  the properties of the  function near  the iterative point. Secondly, combined with improved Wolfe line search, we proposed a Dai-Liao conjugate gradient method based on regularization model. Finally, we proved that the search direction of the proposed 
method satisfied sufficient descent, and established the global convergence of the proposed algorithm under the general assumption. Numerical results show that the proposed algorithm is effective.

We proposed a new nonmonotonic adaptive accelerated Levenberg-Marquardt algorithm for solving nonlinear equations. The algorithm used a new adaptive function to update the Levenberg-Marquardt parameter, which could enhance the consistency between the model and objective function during too-successful iterations, thereby accelerating the convergence rate of the algorithm. Numerical experimental results show that the proposed algorithm has good numerical computational performance.

We considered the modeling problem of complex integer-valued time series data. Firstly, we  proposed a  class of first-order mixed integer-valued negative binomial autoregressive models, proved the strict stationary and ergodicity of the model, and discussed the probabilistic and statistical properties of the model such as transition probability, expectation, variance, etc. Secondly, we studied the  maximum likelihood estimation problem of the model, obtained the asymptotic normality of the estimator, and conducted empirical analysis on the basis of numerical simulations. The empirical analysis results show that the model performs well in fitting the drug offense count data.

We considered a class of fourth-order thin-film equation with singular term and logarithmic source. Firstly, we obtained the local existence of weak solutions to the equation by  combining truncation function and  Galerkin approximation. Secondly, by virtue of the potential well method and Rellich inequality, we proved the global existence and decay estimate of weak solution to the equation under certain conditions. Finally, we proved the blow-up result of the  solution to the equation at a finite time by using the convex method, and gave the lower and upper bounds for blow-up time.

By using the harmonic analysis method and Lagrangian method, we studied the Cauchy problem for the multi-dimensional inhomogeneous incompressible heat-conducting equations and  proved the global well-posedness of strong solutions for the system under small initial data conditions in the critical Besov spaces.

Let (X,d,μ) be a non-homogeneous metric measure space which satisfies the upper doubling and geometrically doubling conditions, and T_α be the generalized fractional integral operator on (X,d,μ). By establishing pointwise inequality of sharp maximum function, we obtain that T_α is bounded from the weighted Lebesgue space L^p(ω) to the weighted weak Lebesgue space WL^p,κ,η(ω), and also from the weighted Morrey space L^p,κ,η(ω) to the weighted weak Morrey space WL^p,κ,η(ω).

By using the divergence theorem and some important inequalities on Riemannian manifolds, combined with  the method of geometric analysis, we studied rigidity problems of compact gradient Ricci-Yamabe solitons, and obtained rigidity result of the nontrivial compact gradient Ricci-Yamabe solitons being equidistant from Euclidean sphere under appropriate conditions. In addition, under the assumption of positive scalar curvature, we proved that n(4≤n≤6) dimensional compact gradient shrinking Ricci-Yamabe solitons that satisfied L^n/2 integral pinched condition must be Einstein manifolds.

Aiming at the problem that  identifying  essential proteins in  biological experiments was time-consuming and laborious, and using
 computational methods to predict essential proteins could not effectively  integrate biological information,  we proposed  a deep learning framework. Firstly, a weighted protein interaction network was constructed by using network topology structure, gene expression data and gene ontology (GO) annotated data. Secondly, feature vectors were extracted from subcellular localization data, protein complex data and gene expression data by using feature graph network and bi-directional long short-term memory cells, respectively. Finally,  these feature vectors were input into the task learning layer to predict essential proteins. The experimental results show that, compared with  existing computational methods, the proposed method has better predictive performance.

Aiming at the problem that the interpretable method based on class activation mapping (CAM) was disturbed by features unrelated to the target class, which led to more noise in the visualization results and lower localization accuracy of target objects, we proposed a convolutional neural network (CNN) visualization method based on ablation analysis. Firstly, the correlation between deep network features and target classes was investigated and feature fusion weights were calculated through ablation experiments. Secondly,  the feature fusion weights were corrected by ReLU or Softmax functions to reduce the interference of irrelevant features and obtain  class activation map with higher localization accuracy, so as to make an effective description of network decisions. A variety of evaluation metrics were used for verification on the ILSVRC 2012 validation set, the experimental results show that the method achieves better model interpretation capability in all indicators.

Aiming at the problem that the existing sequence recommendation model ignored the users’ long-term preference and short-term preference, resulting in the recommendation model not being able to  fully play its role and the recommendation effect being poor, we proposed a personalized recommendation model based on the users’ long- and short-term preferences. Firstly, for the characteristics of long and discontinuous long-term preference sequences, BERT （bidirectional encoder representations from transformers） was used to model the long-term preference, for the short-term preference sequences and the short interval time between interaction with the user, which was volatile, vertical and horizontal convolutional networks were used to model the short-term preference, after obtaining the users’ long-term preference and short-term preference, activation functions were used to model dynamically, and then a gated recurrent network was used to balance the long- and short-term preferences. Secondly, for the users’ mis-touching behavior in daily interaction, sparse attention network was used for modeling, and sparse attention network was used to process the users’ behavioral sequences before modeling the long- and short-term preferences. User feature preferences also had an impact on the recommendation results, and user features were extracted by using a multi-head attention mechanism with bias coding. Finally, the results obtained from each part were input into the fully connected layer to obtain the final output result. In order to verify the feasibility of the proposed model, experiments were conducted on Yelp and MovieLens-1M datasets, and the results show that the proposed model outperforms other baseline models.

Aiming at the problems of insufficient training data and low accuracy of long-tail entity alignment  in the task of knowledge graph entity alignment, we  proposed an iterative entity alignment method based on an adaptive feature fusion strategy and designed an iterative strategy to automatically expand the scale of the training data. This method utilized the structural information of the knowledge graph and utilized  relationships, attributes, and entity name information as  semantic information to assist  alignment 
and  improve alignment effectiveness. The experimental results on the dataset show that the proposed model  performs well in the task of knowledge graph entity alignment.

Aiming at the problem that the cellular Internet of Things involved large-scale device connection and identity authentication management, and attackers cuold use various methods  to forge identity information, which made the difficulty of  anonymous access  user identity authentication increase, the author proposed  an  anonymous access user identity authentication algorithm for cellular Internet of Things. Firstly, the 5G network was used as the dynamic application scenario of the cellular Internet of Things system, and the system parameters were preseted. Secondly, according to the user’s identification number and public key, the forged name was used to generate the user’s anonymous access information, and the registration was anonymously saved to the local. Finally, based on the concept of decentralization, the decryption results of the unit public key and the adjacent group key, the random number encryption information and the unit Hash value were compared to authenticate the user identity. The experimental results show that the proposed algorithm effectively shortens the time required for identity authentication and batch message authentication, reduces the number of bytes required for data transmission, with a time cost of only 13 ms, a computational cost of only 4 ms,  and a communication cost of only 210 bytes. Moreover, it can successfully resist 15 types of identity authentication attacks.

Aiming at the problems that the existing mainstream target detection algorithms had  low detection accuracy and incomplete segmentation in the  image edge regions, we proposed a region of interest pooling algorithm based on Mask RCNN model. Firstly, the feature maps of the regions of interest were divided into edge regions and non-edge regions by the Otsu threshold segmentation method. Secondly, the edge gradient interpolation algorithm was used to interpolate for the edge regions, 
and the bilinear interpolation algorithm was used to interpolate for the non-edge regions so that the discrete feature map was mapped into a continuous space. Thirdly,  the interpolated feature maps were evenly divided into k×k units. Finally, the double integral was used to calculate the average value of each unit to complete the pooling operation. The comparative experimental results show that the proposed algorithm, based on the Mask RCNN model, has a certain improvement in detection accuracy  compared with existing algorithms on COCO(2014) dataset, and has a good segmentation effect on the details of the image edge regions.

Aiming at the problem that existing methods could not fully capture the intrinsic structure of data without considering the higher-order neighborhood information of the data, we proposed an unsupervised feature selection algorithm based on graph filtering and self-representation. Firstly, a higher-order graph filter was applied to the data to obtain its smooth representation, and a regularizer was designed to combine the higher-order graph information for the self-representation matrix learning to capture the intrinsic structure of the data. Secondly, l_2,1 norm was used to reconstruct the error term and feature selection matrix to enhance the 
robustness and row sparsity of the model to select the discriminant features. Finally, an iterative algorithm was applied to effectively solve the proposed objective function and simulation experiments were carried out to verify the effectiveness of the proposed algorithm.

Aiming at the problems of low accuracy, under-detection, and missed detection in the vehicle target detection algorithm at traffic intersections, we proposed a target recognition algorithm of traffic intersection based on improved YOLOv7.  Firstly, the algorithm  used the feed-forward convolutional attention mechanism CBAM to enhance the network’s  attention to key features from both channel attention and spatial attention, improve the network’s running  speed, and optimize the network’s feature extraction capabilities. Secondly, a new learning module was formed by connecting the  spatial layer to depth  layers to form a  full-dimensional dynamic convolution, which improved the YOLOv7 feature learning method and enhanced the feature expression ability. Finally, the experiments were conducted on the actual collected traffic intersection dataset. The experimental results show that the proposed method  achieves an average accuracy of 96.1% on the corresponding dataset, and the training time is reduced to 16.71 h. Therefore, it has obvious recognition advantages  for small target detection at traffic intersections.

Aiming at  the problem of unknown words in speech recognition tasks, we proposed a threshold based-BPE-dropout multi-task learning speech recognition method. This method adopted a random byte pair coding algorithm. When forming sub-words, a strategy with word number threshold was introduced. The sub-words were used as modeling units, and the encoder part adopted Conformer structure, which was combined with link timing classification and attention mechanism. In order to further improve the performance of the model,  dynamic parameters were  introduced to dynamically adjust the loss function, and  multi-task training and decoding were performed simultaneously. The experimental results show that the proposed method can effectively solve the problem of unknown words by using sub-words as modeling units, and further improve the recognition performance of the model under the multi-task learning framework. On the public datasets THCHS30 and ST-CMDS, the model achieves more than 95% recognition accuracy.

Aiming at the problem of insufficient feature extraction resulting in low classification accuracy of the traditional encrypted traffic classification model, we  proposd an encrypted traffic classification model based on an improved convolutional neural network combined with Transformer by using deep learning techniques.  In order to improve the classification accuracy, firstly, we cut and filled the dataset,  and completed standardization processing. Secondly, the multi-head attention mechanism in the Transformer network model was used to capture long-distance feature dependencies, and the convolutional neural network was used to extract local features. Finally, the Inception module was added to achieve multi-dimensional feature extraction and feature fusion, and the model training and encrypted traffic classification were completed. The experimental verification was conducted on the 
ISCX VPN-non-VPN 2016 public dataset, the experimental results show that the classification accuracy of the proposed  model reaches 98.5%, with the precision rate, recall rate and F₁ value  all exceeding  98.2%, which show better classification effect compared with other models.

Aiming at the problem that   multi-source heterogeneous data had the complex sources and unique structure, resulting in a greater difficulty in its fusion. In order to improve the efficiency and accuracy of data fusion, we proposed a multi-source heterogeneous data fusion model based on fuzzy mathematics. Firstly, by utilizing a federated weighted average fusion strategy, the metadata transmitted from various sensors to the data level fusion layer was integrated to obtain the data level fusion results. Secondly, combined with the principal component analysis method and canonical correlation analysis method, the features of data unified by Web Ontology Language were extracted to complete the  feature level data fusion. Thirdly, a fuzzy rule library established and updated based on fuzzy mathematics theory was used to obtain decision level fusion results through decision fusion algorithms. Finally, we combined the data fusion results of above different levels to establish a data fusion model, and obtained the final data fusion result. The experimental results show that the maximum covariance value and absolute error value of the proposed method do not exceed 0.15, and the shortest fusion time is only 12.6 ms. The fusion accuracy and stability of this method are good, and both timeliness and anti-interference have significant advantages.

Aiming at the problem of  the navigational challenges for visually impaired users on diverse webpages, we proposed a method for automatically identifying navigation bars to improve  webpage accessibility. Firstly, by designing heuristic rules, elements within the navigation bars were  autonomously extracted based on the ordered element arrangement within the navigation bar, as well as rules such as hyperlinks and succinct textual content within sub-elements. Secondly, a decision tree binary classification algorithm was used to categorize elements with pronounced feature disparities in the navigation bars. Finally, the identified navigation bar elements were subject to the injection of Landmark attributes. In experimental evaluations of  100 websites, the method successfully identified  92.6% of navigation bar elements, and the infusion of Landmark attributes significantly improves website accessibility, thereby ameliorating the user experience for visually impaired individuals.

Aiming at  the problems that  the whale optimization algorithm was prone to getting stuck in local optima and had drawbacks such as slow  speed control response and large overshoot of brushless DC motor, we  proposed an improved whale optimization algorithm (IWOA) for optimizing proportional integral derivative (PID) parameters in brushless DC motor speed control. The algorithm combined Gaussian mutation factor, adaptive weight factor, and dynamic threshold to optimize the whale optimization algorithm. The simulation experiment results show that the  improved whale optimization  PID speed control algorithm of brushless DC motor has faster  convergence rate, smaller overshoot phenomenon, and better robustness.

We studied the control problem of third-order third-power nonlinear chaotic circuits. Firstly, we gave the Lyapunov exponent and chaotic attractor of the system to verify the existence of complex chaos in the system. Secondly, using adaptive feedback control method and H_∞ state feedback control method, we designed the adaptive feedback controller with known and unknown parameters and H_∞ state feedback controller to stabilize the chaotic system state to the equilibrium point. Finally, the effectiveness of the controller was verified through numerical simulation by using MATLAB software, and the control effect of the two controllers was compared.

By systematically changing the geometric parameters such as pore size and porosity of large and small pores in hierarchically porous membranes, we used finite element simulation method to study the linear or nonlinear quantitative relationships between membrane flux and related geometric parameters. The simulation results show that after addition spherical cavities to the curved channel matrix to form a hierarchical porous structure, the water flux of the film can be increased by about 171% of the original. For the curved channels, simply increasing their number can lead to a linear increase in water flux, and simply increasing their pore size can lead to an exponential function increase in water flux. For spherical cavities,  simply increasing their number or simply increasing their pore size results in an exponential function increase in water flux. In addition, the water flux enhancement effect of spherical cavities also depends on their relative size with the matrix grid of curved channels. The performance of separation membrane materials can be improved by adjusting the preparation conditions.

We designed a wearable wireless plantar pressure acquisition system and proposed a method for determining the stable state of the human body based on the center of pressure (CoP) of the human body. Firstly, the system was used to collect the plantar pressure data in the stable and critical instability states when the human body was standing and walking. Secondly, the area and boundary of the movement locus of the center of pressure in the stable walking state of the human body were obtained through the plantar pressure information. Finally, the CoP at the current moment was collected, and by comparing the trajectory area and boundary range of the CoP at the current moment with the maximum stable CoP of the human body, the stable state judgment of the human walking process was achieved. The results show that the designed wearable wireless plantar pressure acquisition system is wearable and convenient for measuring human plantar pressure data. The experimental verification shows that the human body steady state judgment method based on plantar pressure acquisition system and center of pressure is effective.

Aiming at the problem that it was difficult to eliminate tetracycline in wastewater and achieve water quality purification through self-purification of the environment, we developed and designed a  new type of sewage treatment agents. A novel metal-organic framework (MOF) material [Mn₂(TCPQ)(H₂O)₈]·xsolvent.  was synthesized by 4，4′，4″，4′′′-(quinoxalin-2,3,6,7-tetrayl)tetrabenzoic acid as the organic ligand and Mn(Ⅱ) as the metal center ion. The structure and stability of the material were studied by using powder X-ray diffraction,  X\|ray single crystal diffraction, Fourier transform infrared spectroscopy and thermogravimetry,  and its photocatalytic performance was analyzed. The experimental results show that the degradation rate of tetracycline by the prepared MOFs material can reach 97.5% when exposed to visible light for 30 min. The compound can be used as an excellent  material for the degradation of tetracycline.

The  maltase-glucoamylase (MGAM) from the large fungus Ganoderma lucidum  as the research object,  and a mutant D246A with significantly reduced enzyme activity was successfully constructed by using methods such as homologous sequence alignment,  homologous modeling,  substrate docking,  and site-specific mutation. The characterization results of enzymatic properties show that  the optimal reaction temperature decreases from 65 ℃ for wild type (WT) to 60 ℃， and the heat tolerance of the mutant decreases. The optimal pH value increases from 6.0 for WT to 7.0,  which is beneficial for the growth of engineering bacteria.  The half-life decreases from 2.0 h for WT to 1.5 h,  the stability of enzyme decreases. The enzyme kinetics results show that  the enzyme kinetics curve of mutant D246A conforms to the Michaelis equation, and   compared with the WT, the K_m value increases,  indicating a decrease in affinity of enzyme and substrate.  V_max decreases to 1/4 of its original value.

Based on the microbial degradation mechanism of petroleum contaminated groundwater and the characteristics of low temperature,  low oxygen,  and oligotrophic environments in a certain petroleum contaminated groundwater in Northeast China, we collected  petroleum contaminated groundwater and  studied the efficiency of  indigenous bacteria  degrading petroleum hydrocarbons in petroleum contaminated groundwater stimulated by microbial small molecule substances. The  results show that when petroleum hydrocarbons are used as the sole carbon source and biological small molecule substances such as amino acids and organic phosphorus sources are added to the inorganic salt based nutrient solution,   amino acid substances inhibit the degradation of petroleum hydrocarbons by indigenous bacteria,  with inhibitory ability of glycine (-20.49%)>glutamic acid (-7.81%)>alanine (-4.88%). Organic phosphate lipids promote the degradation of petroleum hydrocarbons by indigenous bacteria,  with promoting ability of lecithin (7.91%)>disodium glycerophosphate (7.01%)>triethyl phosphate (0.03%). Further supplementing biological small molecule carbon sources can improve the degradation efficiency of indigenous bacteria,  with the enhancement ability of sucrose (8.03%)>glucose (6.01%)>maltose (2.91%). Adding inorganic salts,  lecithin,  and sucrose to groundwater with an initial mass concentration   of 10 mg/L of petroleum hydrocarbon， after 7 d of stimulation,  the degradation rate can be increased to 77.26% due to the  stimulation of  biological small molecule substances. Combined with 16SrRNA amplicon sequencing,  high-throughput sequencing is performed on indigenous bacteria before and after the stimulation,  demonstrating that  there is a positive correlation between the abundance of dominant petroleum hydrocarbon genera and the expression of functional genes when biological small molecules promote the synergistic metabolism and degradation of petroleum hydrocarbons by indigenous bacterial communities.